DBSCAN (Density-Based Spatial Clustering of Applications with Noise) finds clusters as dense regions separated by sparse ones. It needs two parameters: a radius ε and a count minPts.

Three kinds of point

• Core: has at least minPts points within radius ε (counting itself).
• Border: within ε of a core point but not itself dense enough.
• Noise: neither — a sparse outlier, drawn as a grey ✕.

Growing a cluster

Pick an unvisited core point and start a cluster. Add every point in its ε-neighbourhood to a queue; for each dequeued point that is itself a core point, add its neighbours too. The cluster keeps expanding through chains of dense points until the frontier is exhausted.

Versus k-means

Unlike k-means, DBSCAN does not need you to pick the number of clusters — it discovers however many dense regions exist. It also follows arbitrary shapes (the Moons and Rings presets are non-convex, where k-means fails) and reports outliers explicitly as noise rather than forcing every point into a cluster.

Choosing ε and minPts

Too small an ε (or too large a minPts) labels everything noise; too large an ε merges everything into one blob. Drag the sliders to feel the trade-off.